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Elementary Abelian \(p\)-groups of rank \(2p+3\) are not CI-groups. (English) Zbl 1294.20069
Summary: For every prime \(p>2\) we exhibit a Cayley graph on \(\mathbb Z_p^{2p+3}\) which is not a CI-graph. This proves that an elementary Abelian \(p\)-group of rank greater than or equal to \(2p+3\) is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra. Moreover, we apply our technique to give a uniform explanation for the recent works of Muzychuk and Spiga concerning the problem.
Reviewer: Reviewer (Berlin)

20K01 Finite abelian groups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Full Text: DOI
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